When data is acquired from an MRI scanner for functional and functional connectivity MRI (f(c) MRI) studies, the temporal resolution of the data is typically low, and the data is plagued with noise from various sources. Of late, parallel MRI reconstruction techniques are often used to increase temporal resolution, and the quality of the reconstructed images is improved through additional data processing operations. However, despite the attractive benefits of these techniques, the implications that each reconstruction and processing operation have on the statistical properties of the data are often unaccounted for. Depending on the operations performed, the covariance structure of processed data can be far removed from that of the original raw data, thereby potentially corrupting the assumptions made about functional activations and connectivity in f(c) MRI studies. As such, it is imperative that scientists have a means of quantifying the effects of image processing and have a means of accounting for them in f(c) MRI models to more accurately and reliably analyze their data. The goals of this study are twofold. In our first aim, we propose to develop a novel approach for observing the correlations artificially induced by image reconstruction, spatial and temporal processing operations by representing each operation in terms of a real-valued matrix operator. With reconstruction and processing operations represented in this fashion, one can exactly determine the correlations induced between all voxels and time points solely by each process. This would allow one to analytically observe the way in which the covariance structure of the originally acquired data is modified through processing without the need for lengthy Monte Carlo simulations. In our second aim, we will incorporate the complete spatiotemporal covariance structure of the processed data, analytically derived through the first aim, into complex-valued f(c) MRI models. This will be done by generalizing existing complex-valued f(c) MRI models to estimate functional activations and connectivity in all voxels of the reconstructed images at once, rather than on a voxel-by-voxel basis that assumes a statistical independence between voxels. Incorporating a complete spatiotemporal covariance structure into generalized f(c) MRI models will decrease the number of false positives incurred solely through processing in functional activation and connectivity estimations. The tools we will develop in our first aim would provide neuroscientists with a means of precisely quantifying the ramifications of commonplace reconstruction and processing operations developed to improve the quality of their data. This would at the very least develop awareness of these implications and provide a tool for characterizing excessive processing in f(c) MRI studies. Incorporating a complete spatiotemporal covariance structure into f(c) MRI models in our second aim would attenuate the effects of artificial correlations that are induced by image reconstruction and processing operations, thereby improving both the accuracy and reliability of conclusions derived in the increasingly popular fields of fMRI and fcMRI.